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In Ezra chapter 2 and Nehemiah chapter 7, we have two very similar lists of family units that returned from Babylon, and the number of members that each group had.
However, many of the numbers between the lists, for the same families, differ.
Also, both lists state the total tally as being 42,360 - but neither list adds up to this tally if one was to individually add them all up.
How can we reconcile these differences?
First, let's address the difference between the total count and the sum of the individual counts given for each family.
Both chapters state that "the whole congregation together" was 42,360:
Ezra 2:64
64 The whole congregation together was forty and two thousand three hundred and threescore,
Nehemiah 7:66
66 The whole congregation together was forty and two thousand three hundred and threescore,
However, if we were to tally the numbers of family members for each family listed, we would arrive thousands short of this number, regardless of which account we are reading.
One solution to this discrepancy would be to point out that many of tallies mention "men" only, and so some or all of the individual tallies may only be counting adult men (heads of households), whereas the whole congregation number includes younger men, and whatever women and children made the journey:
Ezra 2:2
2 Which came with Zerubbabel: Jeshua, Nehemiah, Seraiah, Reelaiah, Mordecai, Bilshan, Mizpar, Bigvai, Rehum, Baanah. The number of the men of the people of Israel:
Nehemiah 7:7
7 Who came with Zerubbabel, Jeshua, Nehemiah, Azariah, Raamiah, Nahamani, Mordecai, Bilshan, Mispereth, Bigvai, Nehum, Baanah. The number, I say, of the men of the people of Israel was this;
We can also recognize that nowhere does giving the "whole congregation" number require that all of the constituents are explicitly listed elsewhere in the chapter. We may have been given only the most important families individually, and the whole number contains even those who did not come from big enough families to warrant an individual entry.
Next, how can we reconcile the fact that different numbers are given for the same group between the two accounts?
The answer to this is that the numbers in Ezra are authoritative. And why do we know that?
We know this because the list in Nehemiah is just from a register that he happened to find:
Nehemiah 7:5
5 And my God put into mine heart to gather together the nobles, and the rulers, and the people, that they might be reckoned by genealogy. And I found a register of the genealogy of them which came up at the first, and found written therein,
Therefore the account in Nehemiah accurately records the register that Nehemiah found. We know from reading the account in Ezra, however, that it was altered.
We can speculate that someone, at some point, had tried to update at least some of the tallies from Ezra, but didn't get to all of the families (some of them match Ezra), nor the total number of the congregation, and this is what Nehemiah found.